A fast variational approach for Bayesian compressive sensing with informative priors

Karseras, Evripidis; Dai, Wei

doi:10.1109/icassp.2014.6854603

Cited by 2 publications

(1 citation statement)

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“…Finally, while we have provided a fast algorithm based on the widely used fast marginal likelihood updates, leveraging recent work performing on SBL inference using approximate message passing [54] or variational methods [55] has the potential to admit implementations of SBL-DF that are highly efficient in high-dimensional settings or more amenable to modifications of the SBL probability model.…”

Section: Discussionmentioning

confidence: 99%

Sparse Bayesian Learning With Dynamic Filtering for Inference of Time-Varying Sparse Signals

O’Shaughnessy

Davenport

Rozell

2020

IEEE Trans. Signal Process.

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Many signal processing applications require estimation of time-varying sparse signals, potentially with the knowledge of an imperfect dynamics model. In this paper, we propose an algorithm for dynamic filtering of time-varying sparse signals based on the sparse Bayesian learning (SBL) framework. The key idea underlying the algorithm, termed SBL-DF, is the incorporation of a signal prediction generated from a dynamics model and estimates of previous time steps into the hyperpriors of the SBL probability model. The proposed algorithm is online, robust to imperfect dynamics models (due to the propagation of dynamics information through higher-order statistics), robust to certain undesirable dictionary properties such as coherence (due to properties of the SBL framework), allows the use of arbitrary dynamics models, and requires the tuning of fewer parameters than many other dynamic filtering algorithms do. We also extend the fast marginal likelihood SBL inference procedure to the informative hyperprior setting to create a particularly efficient version of the SBL-DF algorithm. Numerical simulations show that SBL-DF converges much faster and to more accurate solutions than standard SBL and other dynamical filtering algorithms. In particular, we show that SBL-DF outperforms state of the art algorithms when the dictionary contains the challenging coherence and column scaling structure found in many practical applications.

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Section: Discussionmentioning

confidence: 99%